It takes practice. I remember failing the puzzle about ten times in a row before finally succeeding the first time. Now I succeed about 90% of the time (when I bother opening silver chests at all). Honestly, unless you are a crafter who obsessively collects every reagent you come across, silver chests aren't really worth the time to open them.
Some hints: 1) You will almost always need at least half the tiles revealed, spam click hidden tiles as quickly as you can at the start without worrying about what you uncover. When you have 3 or 4 rows revealed then start looking for the tiles you actually need.
2) Put a couple of "slow" zig-zag tiles next to the left hand plug, the spark will take a little while to travel through those and give you more time to work.
3) You always need more horizontal straight line tiles than anything else.
4) I always build a track of horizontal lines straight across the puzzle, put in one up or down turn at the right edge, add as many vertical straight lines as needed, then finish with a final turn into the right plug. Develop a system like this and stick to it, getting creative with the path just wastes time.
5) The 90 degree turn tiles can be a bit hard to intuitively identify correctly. I have found it easiest to think of the turn tiles as "arrows" that "point" in one of the four diagonal directions, it makes it easier to scan for a correct turn tile in the pool of revealed tiles.